How can I bake the cloth simulation into keyframed vertices or shape keyed vertices?
If you look in the Modifiers section of the properties you will see an Apply button (you probably don't want that one) and an Apply as Shape Key button.  That's the one you want.

After you have turned the cloth shape into a Shape Key, you will have to go to the mesh section and dial up the influence of the new Cloth shape key to 1.0 to change the cloth into the shape that you "baked".